Direct measurements of the stellar magnetic fields are based on the splitting of spectral lines into polarized Zeeman components. With few exceptions, Zeeman signatures are hidden in data noise and a number of methods have been developed to measure the average, over the visible stellar disk, of longitudinal components of the magnetic field. As to faint stars, at present observable only with low resolution spectropolarimetry, a method is based on the regression of the Stokes V signal against the first derivative of Stokes I. Here we present an extension of this method to obtain a direct measurement of the transverse component of stellar magnetic fields by the regression of high resolution Stokes Q and U as a function of the second derivative of Stokes I. We also show that it is possible to determine the orientation in the sky of the rotation axis of a star on the basis of the periodic variability of the transverse component due to its rotation. The method is applied to data, obtained with the Catania Astrophysical Observatory Spectropolarimeter, along the rotational period of the well known magnetic star b{eta} CrB.
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